Recent works in swarm robustness have considered robustness as collective resistance
to sensor and actuator noise. The effect of Gaussian noise distributions on
collective swarm motion was measured and empirically analyzed
by [1]}, [2]}.
It was shown that swarms in general are able to adapt and overcome Gaussian
distributed noise with \(\sigma =\pm ~\frac{\pi }{2}\)  in many cases, but for
\(\sigma =\pm \pi \)  or greater, only small swarms are able to
adapt [1]}. Gaussian noise distributions were applied to robot sensor
readings in [4]}, and their effects studied for different variants of adaptive
response threshold foraging algorithm. The Fokker-Planck equation was
derived from statistical physics for a given Langevin equation governing robot
motion, including noise models, and applied to the analysis of simple phototaxis
behaviors [5]}. Other
works inject a small level of uniform or Gaussian noise (0.5–10%) to help narrow the
simulation-reality gap, without performing statistical
analysis ([6]}, [7]}). Many theoretic works
do not incorporate noise into their models ([8]}, [9]}, [10]}, [11]}); exceptions
include [1]}. Similarly, many application oriented works do not
systematically evaluate algorithms in the presence of
noise ([13]}, [14]}, [15]});
exceptions include [4]}.
